GIVE me thirty kids, a circle of chairs and twenty minutes. I’ll then drop in, uninvited, on a couple of other classes, chat to the dinner ladies and secretary, wander round the playground at break, count the seagulls, and have my Ofsted report on the head’s desk by lunchtime.

The bit with the chairs is a group practical test that says more about scholars’ aptitudes and attitudes than any three-hour written exam ever could.

“I’m going to remain seated here. If you’re Mark, Mary or Max, you’ll end up on one of the seats immediately to my left. On this side, there’ll probably be a Luke, Lucy or Louise. Clockwise in alphabetical order of your forenames. Go.”

A colleague and I do this at the start of workshops we run for young people. A second exercise, which able youngsters complete quicker, requires them to sit according to their birthdays. Year 7 will be as comfortable, or not, with the tasks as those in Year 11.

Almost invariably, the circle contains two people with the same birthday.

There’s a mathematical probability formula. It’s more likely than not that there’ll be two people sharing a birthday once the group size reaches 23.

I wonder what would happen if professional football teams and referees did this round the centre circle just before kick-off. Perhaps there’d be fewer red and yellow cards…

In order to protect two delightful lads whose misdemeanour was so charming nobody could surely want them to be punished for it, decades later, I’m going to call them Peter and James: identical twins who always dressed alike, spoke alike, and generally behaved in such a manner that even their best friends had difficulty telling who was who.

Back in the 1980s, when students would be entered for either a GCE or CSE exam, Peter, the more able mathematician, sat the latter on his brother’s behalf, gaining him an O-level equivalent by gaining a grade A.

I’ve not been able to confirm that James repaid this kindness by passing his brother’s driving test a few years later.